The chap from the future, who ran the Looper business, told them. Presumably he was sent other missives from the future. We know they can send back ordinary materials (eg silver and gold, and clothing) so they could send him written notes on paper. Probably they limit the information they send so as to minimise risk of paradoxes.

For me that was less a plot-hole, and more a detail they didn't bother to fill in because it was both obvious and unimportant. I'm more bothered by the premise (ie, of all things, why use the time-travel for that), and by the apparent lack of consistency:

Spoiler

If you can't kill people in the future, why carry guns around? Why allow Bruce Willis' wife to get killed like that?

Why not give the victims a lethal injection just before sending them back, so their heart stops a few minutes after they arrive? Making them unconscious first would also seem a wise move.

Spoiler

You can kill people, it's just difficult to dipose of the bodies. I guess when it comes to organised crime, it's going to be syndicate vs syndicate based in the same city or in the 5 major cities as described in the film. These sorts of murders are going to have obvious perpertrators or the perps are going to be from within an obvious group of people. A random women in China is going to be harder to connect.

There's less guarentees with that method, you would be sending someone into the unknown. At least with this method there is someone at the other end to confirm what has happened. Plus the people in the future would be directly responsible for the murder, I guess this is the main reason why they send people back. So they aren't directly responsible.

Why try and justify the methods of someone who is runs a organised crime syndicate who will probably be unhinged anyway!